Solution:

If the Earth's radius shrinks to half, but its mass remains the same, the orbital period of the satellite will not change.

The orbital period \( T \) of a satellite depends on the mass of the Earth \( M \) and the radius of the orbit \( r \), not the radius of the Earth itself. The formula for the period of a satellite in orbit is:

\[
T = 2\pi \sqrt{\frac{r^3}{GM}}
\]

Since the mass \( M \) of the Earth and the radius \( r \) of the satellite’s orbit (which is unaffected by the Earth shrinking) remain the same, the period \( T \) remains unchanged.

Thus, the new period of revolution will still be \( T \).